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Kirchhoff's Laws
Kirchhoff's circuit laws are two equalities that deal with
the conservation of charge and energy in electrical circuits
...
Kirchhoff's current law (KCL) – Based on principle of
conservation of electric charge
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Kirchhoff's voltage law (KVL) - Based on principle of
conservation of energy
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The principle of conservation of electric charge implies that: At
any node (junction) in an electrical circuit, the sum of currents
flowing into that node is equal to the sum of currents flowing
out of that node, or The algebraic sum of currents in a network
of conductors meeting at a point is zero
...

However, for AC circuits having dimensions much
smaller than a wavelength, KCL is also approximately
applicable
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i1 + i4 =i2 + i3 Recalling that current is
a signed (positive or negative) quantity reflecting
direction towards or away from a node, this principle can
be stated as:

I

0

Kirchhoff's voltage law (KVL)
 This law is also called Kirchhoff's second law,
Kirchhoff's loop (or mesh) rule, and Kirchhoff's second
rule
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 However, for AC circuits having dimensions much smaller
than a wavelength, KVL is also approximately applicable
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Similarly to KCL, it can
be stated as:

Vemf

I

R

OR

KVL

V0

loop

The sum of all the voltages around the loop is equal to
zero
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Planar
circuits are circuits that can be drawn on a plane surface
with no wires crossing each other
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An essential mesh is a loop in the
circuit that does not contain any other loop
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Assign mesh currents i1, i2,
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Current
direction need to be same in all meshes either clockwise
or anticlockwise
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Apply KVLto each of the n meshes
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3
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Apply KVL to each mesh
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R1

R3
R3

R3
i1
R2 R3 i2

V1
V2

Use i for a mesh current and I for a branch
current
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3
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 Nodal analysis is possible when all the circuit
elements branch constitutive relations have an
admittance representation
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STEPS FOR NODAL ANALYSIS:• Note all connected wire segments in the circuit
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• Select one node as the ground reference
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Choosing
the node with most connections can simplify the analysis
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If
the voltage is already known, it is not necessary to assign a
variable
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Basically, add together all currents
leaving from the node and mark the sum equal to zero
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The
currents of the two nodes are combined in a single
equation, and a new equation for the voltages is
formed
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1
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Choose a reference (ground) node
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Assign node voltages to the other nodes
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Apply KCL to each node other than the reference
node; express currents in terms of node voltages
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Solve the resulting system of linear equations for the
nodal voltages
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KCL at Node 1
V1

I1

500

500

V2

I1

V1 V2
500

V1
500

3
...
KCL at Node 3
V2

500

V3

500

I2

V3 V2
500

V3
500

I2



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